Abstract:The nonlinear eigenvalue problem for p-Laplacian $$ \cases - div (a(x) |\nabla u|^{p-2} \nabla u) = \lambda g (x) |u|^{p-2} u \text { in } \Bbb R^N, u >0 \text { in } \Bbb R^N, \lim _{|x|\to \infty } u(x) = 0, \endcases $$ is considered. We assume that $1 < p < N$ and that $g$ is indefinite weight function. The existence and $C^{1, \alpha }$-regularity of the weak solution is proved.
Keywords: eigenvalue, the p-Laplacian, indefinite weight, regularity
AMS Subject Classification: Primary 35P30, 35J70